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I have the following data set:
dependent variable
Yellow Skin,Yellow Eyes,Yellow Nails,Yellow Tongue,Dark Urine,Abdominal Pain,Nausea & Vomiting After Meal,Loss of Appetite,Fatigue & Weakness,Fever, Flu,Headach,Pale colored stools,Gender,Age (Years)
Independent Variable
What do you suggest which algorithm shuld I use for prediction ? and Why ?
For example I am thinking to apply Logistic regression, support vector machine and backpropagation neural network. Should I not try decision tree or other algorithms if not then why? 
I am little confused with which algorithm should I try

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Did you mix up your dependent and independent variables? Logistic Regression is best for communicating results, removes the black box element of a neural network and the weights for each independent variable is very obvious from the output.

Yes that is a small typo error. So you are suggesting to use Logistic regression


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